This invention relates to a household electrical steam generator with stabilized boiler water level, particularly for smoothing irons. Steam is known to be increasingly used in modern homes, namely for floor, armchair, bath and curtain cleaning, and in particular for ironing. Such steam is generally produced in a water container comprising an electrical resistance heater, the heat of which vaporizes the water until temperature sensors (thermostats) or pressure sensors (pressure switches) deactivate it to prevent explosion deriving from excess pressure. The widespread domestic use of steam has led to a considerable technological development of this sector, such that there currently exist a large number of technical expedients aimed at creating increasingly more perfect and more economical household electrical steam generators, with the scope of leading the commercial competition between the numerous manufacturers. Hence just small details can make that added difference defining an excellent product offering low cost and high performance. For their periodical filling with water, most boilers are provided with a robust plug which is screwed into and unscrewed from the boiler body. To prevent burn-out of the water-heating electrical resistance element as a result of its excessive temperature rise, devices are used for indicating an insufficient water quantity remaining in the boiler. Following this indication, the boiler plug must be unscrewed and a given quantity of cold water poured into the boiler. Because the residual water itself generates steam, this plug unscrewing becomes a dangerous operation as the violent steam exit can scald the hands. There is a like danger in pouring the cold water into the boiler, because its contact with the very hot walls can result in spitting causing scalding. This typical method of filling usual boilers has a further serious drawback, namely that of feeding into the boiler a large quantity of cold water which requires a considerable time to be heated and converted into steam. This results in a non-continuous steam availability. To reduce the number of fillings, the boiler would have to be very large, but this theoretical solution has limits not only because of the said drawback of the lengthy waiting time for the water to be heated, but also because of the fact that the larger the internal volume of the boiler, the greater the elastic energy which it can contain and hence the greater the danger in the case of explosion. Moreover the greater the boiler volume the greater must its wall thickness be for the same pressure as a smaller boiler. This means a greater boiler cost and a weight which becomes inconvenient. To avoid these drawbacks, various technical attempts have been made to separate the actual boiler from the cold water reservoir, but these have proved unsatisfactory from the cost and reliability viewpoint. In these types of generator there is moreover the drawback that the pump forms a "channel" for water transit from the reservoir to the boiler when this latter is subjected to the typical vacuum caused by cooling. In this respect, this causes excessive water filling of the boiler which, when the boiler is again switched on not only results in an increased heating time, but also in initial very hot water spitting before steam can be emitted at the correct quality. This spitting is caused by the reduction or absence, in the boiler, of a free water surface necessary for its vaporization. In most boilers, the heating resistance element is switched on and off by usual bimetallic thermostats, or by pressure switches which deactivate it on reaching a limiting pressure which must not be exceeded in order not to risk explosion. However these control devices have too wide a range of action and are of poor reliability, and are hence unsatisfactory.